A. There was my father, with tears in his eyes.
B. There was my father with tears in his eyes.
Given sentences A and B, is sentence A only grammatical because, without the comma, sentence B can imply that there were more than one father?
So, is sentence A, where "with tears in his eyes", which is set off by the comma, as non-restrictive information, qualifies "my father", correct English if there was only one father?
I think that on the condition that there was only one father, sentence A only is grammatical and correct English.
If I'm right, is sentence C below correct English as well?
C. There was a woman next to my father, with tears in his eyes.
Here, "with tears in his eyes", as a non-restrictive information, qualifies "my father"